I suspect this has to do with branches of complex functions. I tried
using both Mathematica and the Schaum answer on definite integrals, e.g.
{x,1,2}, and got the same answers. Without spending a lot of time, I do
not see how to easily find the relationship between the two answers.
Kevin
"J.R. Chaffer" wrote:
>
> Hi, this newbie gets erroneous results with Mathematica
> 4.0 (for students), with the following integral. Hopefully
> someone can tell me why, and what I may be doing
> wrong. I have tried "Assumptions -> x e Reals", or
> x > 0, with same results. Integral in question is,
>
> Integrate[1/Sqrt[1-Sin[2x]]]
>
> The result is somewhat involved, instead of the expected
> result (Schaum, "Calculus" 4E, p. 297),
>
> integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]]
>
> One expects to get differing forms with any computer
> algebra system, since there are so many equivalent forms
> of algebraic expressions. However, Mathematica's form
> and the Schaum (correct) form differ by significant
> numerical values, as plotting shows (i.e., not some E-16
> or some such).
>
> Further, and what really seems wrong, is that when one
> differentiates Mathematica's result for the integral, one
> does NOT get the original integrand, or anything even
> close, numerically.
>
> So, I am confused. Anyone who knows the explanation
> would be welcome to share it.
>
> Thank you.
>
> John Chaffer